Strength of signal isn't used because strength is an unreliable measure of distance. The amount of atmosphere the signal passes through, reflection/refraction and all manner of weather effects will modify a signal's strength. So the sats transmit a pulse at a pre-agreed time and the receivers use the timing that they receive the signal as the measure of distance.

> based on the strength of that signal

No, GPS positioning uses the precise time information encoded in the data from the satellites.

> Your receiver is just listening to the broadcast signal from several (usually 4+) satellites and based on the strength of that signal determining how far it is from each of those satellites.

GPS doesn't use the strength of the signal at all. Instead, each signal contains precise information about the current time at the highly-accurate atomic clocks onboard the corresponding satellite (plus some important metadata about each satellite, including things like their orbit parameters). If the receiver already knew the precise time, it could calculate the distance to each satellite from the difference between the true time and the received time (and the speed of the light), and 3 satellites would be enough to triangulate its position. Since the receiver usually doesn't know the precise time, it needs an extra satellite because there are now 4 unknowns (3 for its position plus 1 for the current time).

(Obviously, that's a very simplified explanation, there are plenty of other things which complicate the calculations.)

>and based on the strength of that signal

Wrong. Utterly wrong.